Improvements in motor sequence learning come about via goal-based learning of the sequence of visual stimuli and muscle-based learning of the sequence of movement responses. In young adults, consolidation of goal-based learning is observed after intervals of sleep but not following wake, whereas consolidation of muscle-based learning is greater following intervals with wake compared to sleep. While the benefit of sleep on motor sequence learning has been shown to decline with age, how sleep contributes to consolidation of goal-based vs. muscle-based learning in older adults (OA) has not been disentangled. We trained young (n = 62) and older (n = 50) adults on a motor sequence learning task and re-tested learning following 12 h intervals containing overnight sleep or daytime wake. To probe consolidation of goal-based learning of the sequence, half of the participants were re-tested in a configuration in which the stimulus sequence was the same but, due to a shift in stimulus-response mapping, the movement response sequence differed. To probe consolidation of muscle-based learning, the remaining participants were tested in a configuration in which the stimulus sequence was novel, but now the sequence of movements used for responding was unchanged. In young adults, there was a significant condition (goal-based vs. muscle-based learning) by interval (sleep vs. wake) interaction, F(1,58) = 6.58, p = 0.013: goal-based learning tended to be greater following sleep compared to wake, t(29) = 1.47, p = 0.072. Conversely, muscle-based learning was greater following wake than sleep, t(29) = 2.11, p = 0.021. Unlike young adults, this interaction was not significant in OA, F(1,46) = 0.04, p = 0.84, nor was there a main effect of interval, F(1,46) = 1.14, p = 0.29. Thus, OA do not preferentially consolidate sequence learning over wake or sleep.